No you can safely remove them.
You will need to look at the theme templates folder for the template file spTopicView.php
If you take a little time to read through that – you don’t really need php skills just look at the function names – you will see how each page element displays and should be able to find the ones you want to remove.
As always we recommend making your own theme rather than editing a supplief one which can be overwritten when we provide an update.

Slightly related – Why not do away with the button altogether and use the post number as the permalink?

We use the post_id as the permalink and even that is is inly a tag (fragment) not actually a part of the url. The post number is simply a helpful sequence and can change – i.e., when a post is deleted or moved to another topic.
The permalink button is simply a way to help users copy the url to a post…
Or am I missing your point?

Target the square button with the post number in it for the action in place of the square button with the link icon and remove the button with the link icon. Seems intuitive to me as a long time user of forums.

Dave H – putting the “simple” in Simple Press one tiny suggestion at a time! 🙂

both the permalink button and the print button are simple template tags in the theme template file… simply remove the calls and they are gone…